核形状演化中四极-十六极关联的半经典描述
Semiclassical description of quadrupole-hexadecapole correlation in nuclear shape evolution
- Nagoya Institute of Technology（名古屋工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
利用半经典周期轨道理论，通过空腔模型中轨道分岔解释核形状演化中四极-十六极关联，揭示十六极形状系统性与长椭球优势机制。
AI中文摘要：
背景：利用真实有效相互作用或平均场势进行的核形状理论研究已表明，十六极形状演化随粒子数变化呈现出显著的系统性规律：在每个单粒子壳层内，从一个球形幻数到下一个幻数，前半部分出现菱形类型（β_4>0），随后在后半部分转变为长椭球类型（β_4<0）。目的：核形变本质上由单粒子壳层结构决定。在半经典周期轨道理论（POT）中，能级密度表示为经典周期轨道贡献之和，而粗壳结构的起源可通过一个或少数最短轨道的贡献来理解。利用POT，我考察十六极自由度如何通过轨道分岔影响轨道对形变壳结构的贡献，以解释上述形状演化的机制。方法：通过壳修正方法系统研究基态形变，考虑轴对称四极和十六极形状自由度。为简化起见，我采用两种最简单的平均场势来获得壳修正：谐振子势和空腔（无限深势阱）势。在确认这些最简单平均场模型下形状演化的系统性之后，进行半经典分析，重点关注周期轨道分岔的作用。结果与结论：每个单粒子壳层中十六极形状演化的系统性可由空腔模型中两类不同周期轨道的分岔清晰解释，这表明四极与十六极参数之间存在强关联。这也确保了在该简单势模型内核长椭球形状优势的机制。
英文摘要：
Background: Theoretical investigations of nuclear shapes with realistic effective interactions or mean field potentials have suggested a remarkable systematics in the hexadecapole shape evolution with varying particle number: Within each single-particle shell, from one spherical magic number to the next, a diamond type (beta_4>0) appears in the first half, and then turn into oblong type (beta_4<0) in the second half. Purpose: Nuclear deformation is essentially governed by the single-particle shell structure. In semiclassical periodic orbit theory (POT), level density is expressed as the sum over contributions from classical periodic orbits, and the origins of the gross shell structures can be understood by the contribution of one or a few shortest orbits. Using the POT, I examine how the hexadecapole degree of freedom affect the contribution of the orbits to the deformed shell structure through their bifurcations to explain the mechanism of above shape evolution. Methods: Ground state deformations are systematically investigated by the shell correction method, taking account of axially symmetric quadrupole and hexadecapole shape degrees of freedom. For simplicity, I employ two simplest mean field potentials to obtain the shell corrections: the oscillator and the cavity (infinite well) potentials. After confirming the the systematics in shape evolution under these simplest mean-field models, semiclassical analyses are made, focusing on the role of PO bifurcation. Results and conclusions: Systematics in the hexadecapole shape evolution in each single-particle shell is clearly explained by the bifurcations of two different types of periodic orbits in the cavity model, which suggest strong correlation between quadrupole and hexadecapole parameters. This also ensures the mechanism of nuclear prolate-shape predominance within this simple potential model.
